Boats and Streams Quiz 1

Solution - -
Down speed = \frac{40}{48} \times 60 = 50km/hr
4:1 =4x:x
Downstream speed = 4x+x=5x
Upstream speed = 4x-x=3x
5x= 50; x=10
so up speed 3\times10=30
Time = \frac{30}{30} \times 60 = 60 mins

Solution -
Downstream speed = 80/10 = 8 km/hr
Upstream speed = 80/20 = 4 km/hr
So speed of stream = \frac{1}{2}\times \left ( 8-4 \right )=2km/hr

Solution -
Speed downstream = \frac{5}{x}
Speed upstream = \frac{4}{x}
\frac{40}{\frac{5}{x}}+\frac{40}{\frac{4}{x}}=9
X = \frac{1}{2}
So, Speed downstream = 10 km/hr, Speed upstream = 8 km/hr
Rate of the stream = \frac{1}{2}\times 2= 1 km/hr

Solution -
Rate downstream =\frac{1}{6}\times 60=10kmph
Rate upstream = 5 km/hr.
Speed in still water =\frac{1}{2}\times 15=7.5kmph
Required time = \frac{15}{7.5}=2 hrs

Solution:
From the data, upstream speed=\frac{40}{10}=4kmph
And, downstream speed=\frac{40}{20}=2 kmph
So, the speed of the boat=\frac{1}{2}\left ( 4+2 \right )=3kmph

Solution:
Downstream speed of the boat= (15 + 5)= 20 km/hr.
Time taken by the boat to go 80 km downstream= (80/20) hours= 4 hrs.

Solution:
Downstream speed of the boat= (7.5 + 2.5)= 10 km/hr.
Time taken by the boat to go 40 km downstream= (40/10) hours= 4 hrs.

Solution - Rowing speed of Alex in still water= (Rate upstream + Rate Downstream)
= \frac{1}{2}\left ( 7+3\right )=5
And rate of the current=\frac{1}{2}\left ( 7-3\right )=2

Solution -
Since it is mentioned that his speed downstream is twice that of the upstream.
So let Sam’s speed upstream be ‘a’ then his speed downstream= 2a
Therefore (2a+a)= 10 or a= 6.66 kmph
Hence his speed upstream= 6.66 kmph and
His speed downstream= 6.66\times 2= 13.33 kmph
Therefore the rate of the current= 3.33 kmph

Solution - Let the speed of the boat in still water be
Sam takes 12.5 minutes 750 seconds to cover 900 m upstream
Therefore speed upstream= 900/750 = 1.2 mps
As the time taken downstream 7.5 min or 450 sec
Therefore speed downstream = 900/450= 2 mps
Therefore speed in stable water= \frac{1}{2}\left ( 1.2+2\right )=1.6mps
Or \frac{3600}{1000}\left ( 1.6\right )=5.76 kmph